Answer:
The simplest radical form is [tex]9\sqrt{5}[/tex] ⇒ (c)
Step-by-step explanation:
To simplify any square root;
- Factorize the number under the root using prime numbers
- Take out the root any number repeated twice as one number
Examples:
1. Simplify [tex]\sqrt{8}[/tex]
factorize 8 using prime numbers
8 = 2 × 2 × 2, then [tex]\sqrt{8}=\sqrt{(2)(2)(2)}[/tex]
Take two of 2 out the root, then [tex]\sqrt{8}=2\sqrt{2}[/tex]
2. Simplify [tex]\sqrt{18}[/tex]
factorize 18 using prime numbers
18 = 2 × 3 × 3, then [tex]\sqrt{18}=\sqrt{(2)(3)(3)}[/tex]
Take the two 3 out the root, then [tex]\sqrt{18}=3\sqrt{2}[/tex]
Let us simplify [tex]3\sqrt{45}[/tex]
∵ 45 = 3 × 3 × 5
∴ [tex]3\sqrt{45}=3\sqrt{(3)(3)(5)}[/tex]
→ Take the two 3 out by one 3
∴ [tex]3\sqrt{45}=3(3)\sqrt{5}[/tex]
→ Multiply the numbers out the root
∴ [tex]3\sqrt{45}=9\sqrt{5}[/tex]
∴ The simplest radical form is [tex]9\sqrt{5}[/tex]
